The Optimal Control of Government Stabilization Funds

Abstract

We study the optimal control of a government stabilization fund, which is a mechanism to save money during good economic times to be used in bad economic times. The objective of the fund manager is to keep the fund as close as possible to a predetermined target. Accordingly, we consider a running cost associated with the difference between the actual fiscal fund and the fund target. The fund manager exerts control over the fund by making deposits in or withdrawals from the fund. The withdrawals are used to pay public debt or to finance government programs. We obtain, for the first time in the literature, the optimal band for the government stabilization fund. Our results are of interest to practitioners. For instance, we find that the higher the volatility, the larger the size of the optimal band. In particular, each country and state should have its own optimal fund band, in contrast to the “one-size-fits-all” approach that is often used in practice.

The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method

“…On the other hand, according to Equation ( 18), an admissible process (x, u) can be evaluated over the sub-interval (t 1 , t f ) by: 11) and ( 12) to the given u and g. Obviously, in this case, Equations ( 21) and ( 22) solved for  and ĝ are equivalent to Equations (11) and (12). Theorem 3 reveals that each state-dependent-term on the right-hand side of Equation ( 27) is equal to a corresponding component of Jeq .…”

“…For the latter, the problem is addressed in the framework of optimal control theory. The fundamental objective in this field is to maximize the return from, or minimize the cost of, the operation of physical [3,4], biological [5,6], social [7][8][9], economic processes [10,11], etc.…”